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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math.optimization.general;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math.FunctionEvaluationException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math.MaxEvaluationsExceededException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math.MaxIterationsExceededException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math.analysis.MultivariateMatrixFunction;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math.linear.InvalidMatrixException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math.linear.LUDecompositionImpl;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math.linear.MatrixUtils;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math.linear.RealMatrix;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math.optimization.OptimizationException;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math.optimization.SimpleVectorialValueChecker;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math.optimization.VectorialConvergenceChecker;<a name="line.31"></a>
<FONT color="green">032</FONT>    import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer;<a name="line.32"></a>
<FONT color="green">033</FONT>    import org.apache.commons.math.optimization.VectorialPointValuePair;<a name="line.33"></a>
<FONT color="green">034</FONT>    <a name="line.34"></a>
<FONT color="green">035</FONT>    /**<a name="line.35"></a>
<FONT color="green">036</FONT>     * Base class for implementing least squares optimizers.<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;p&gt;This base class handles the boilerplate methods associated to thresholds<a name="line.37"></a>
<FONT color="green">038</FONT>     * settings, jacobian and error estimation.&lt;/p&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * @version $Revision: 786466 $ $Date: 2009-06-19 08:03:14 -0400 (Fri, 19 Jun 2009) $<a name="line.39"></a>
<FONT color="green">040</FONT>     * @since 1.2<a name="line.40"></a>
<FONT color="green">041</FONT>     *<a name="line.41"></a>
<FONT color="green">042</FONT>     */<a name="line.42"></a>
<FONT color="green">043</FONT>    public abstract class AbstractLeastSquaresOptimizer implements DifferentiableMultivariateVectorialOptimizer {<a name="line.43"></a>
<FONT color="green">044</FONT>    <a name="line.44"></a>
<FONT color="green">045</FONT>        /** Default maximal number of iterations allowed. */<a name="line.45"></a>
<FONT color="green">046</FONT>        public static final int DEFAULT_MAX_ITERATIONS = 100;<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>        /** Maximal number of iterations allowed. */<a name="line.48"></a>
<FONT color="green">049</FONT>        private int maxIterations;<a name="line.49"></a>
<FONT color="green">050</FONT>    <a name="line.50"></a>
<FONT color="green">051</FONT>        /** Number of iterations already performed. */<a name="line.51"></a>
<FONT color="green">052</FONT>        private int iterations;<a name="line.52"></a>
<FONT color="green">053</FONT>    <a name="line.53"></a>
<FONT color="green">054</FONT>        /** Maximal number of evaluations allowed. */<a name="line.54"></a>
<FONT color="green">055</FONT>        private int maxEvaluations;<a name="line.55"></a>
<FONT color="green">056</FONT>    <a name="line.56"></a>
<FONT color="green">057</FONT>        /** Number of evaluations already performed. */<a name="line.57"></a>
<FONT color="green">058</FONT>        private int objectiveEvaluations;<a name="line.58"></a>
<FONT color="green">059</FONT>    <a name="line.59"></a>
<FONT color="green">060</FONT>        /** Number of jacobian evaluations. */<a name="line.60"></a>
<FONT color="green">061</FONT>        private int jacobianEvaluations;<a name="line.61"></a>
<FONT color="green">062</FONT>    <a name="line.62"></a>
<FONT color="green">063</FONT>        /** Convergence checker. */<a name="line.63"></a>
<FONT color="green">064</FONT>        protected VectorialConvergenceChecker checker;<a name="line.64"></a>
<FONT color="green">065</FONT>    <a name="line.65"></a>
<FONT color="green">066</FONT>        /** <a name="line.66"></a>
<FONT color="green">067</FONT>         * Jacobian matrix.<a name="line.67"></a>
<FONT color="green">068</FONT>         * &lt;p&gt;This matrix is in canonical form just after the calls to<a name="line.68"></a>
<FONT color="green">069</FONT>         * {@link #updateJacobian()}, but may be modified by the solver<a name="line.69"></a>
<FONT color="green">070</FONT>         * in the derived class (the {@link LevenbergMarquardtOptimizer<a name="line.70"></a>
<FONT color="green">071</FONT>         * Levenberg-Marquardt optimizer} does this).&lt;/p&gt;<a name="line.71"></a>
<FONT color="green">072</FONT>         */<a name="line.72"></a>
<FONT color="green">073</FONT>        protected double[][] jacobian;<a name="line.73"></a>
<FONT color="green">074</FONT>    <a name="line.74"></a>
<FONT color="green">075</FONT>        /** Number of columns of the jacobian matrix. */<a name="line.75"></a>
<FONT color="green">076</FONT>        protected int cols;<a name="line.76"></a>
<FONT color="green">077</FONT>    <a name="line.77"></a>
<FONT color="green">078</FONT>        /** Number of rows of the jacobian matrix. */<a name="line.78"></a>
<FONT color="green">079</FONT>        protected int rows;<a name="line.79"></a>
<FONT color="green">080</FONT>    <a name="line.80"></a>
<FONT color="green">081</FONT>        /** Objective function. */<a name="line.81"></a>
<FONT color="green">082</FONT>        private DifferentiableMultivariateVectorialFunction f;<a name="line.82"></a>
<FONT color="green">083</FONT>    <a name="line.83"></a>
<FONT color="green">084</FONT>        /** Objective function derivatives. */<a name="line.84"></a>
<FONT color="green">085</FONT>        private MultivariateMatrixFunction jF;<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>        /** Target value for the objective functions at optimum. */<a name="line.87"></a>
<FONT color="green">088</FONT>        protected double[] target;<a name="line.88"></a>
<FONT color="green">089</FONT>    <a name="line.89"></a>
<FONT color="green">090</FONT>        /** Weight for the least squares cost computation. */<a name="line.90"></a>
<FONT color="green">091</FONT>        protected double[] weights;<a name="line.91"></a>
<FONT color="green">092</FONT>    <a name="line.92"></a>
<FONT color="green">093</FONT>        /** Current point. */<a name="line.93"></a>
<FONT color="green">094</FONT>        protected double[] point;<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>        /** Current objective function value. */<a name="line.96"></a>
<FONT color="green">097</FONT>        protected double[] objective;<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>        /** Current residuals. */<a name="line.99"></a>
<FONT color="green">100</FONT>        protected double[] residuals;<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>        /** Cost value (square root of the sum of the residuals). */<a name="line.102"></a>
<FONT color="green">103</FONT>        protected double cost;<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>        /** Simple constructor with default settings.<a name="line.105"></a>
<FONT color="green">106</FONT>         * &lt;p&gt;The convergence check is set to a {@link SimpleVectorialValueChecker}<a name="line.106"></a>
<FONT color="green">107</FONT>         * and the maximal number of evaluation is set to its default value.&lt;/p&gt;<a name="line.107"></a>
<FONT color="green">108</FONT>         */<a name="line.108"></a>
<FONT color="green">109</FONT>        protected AbstractLeastSquaresOptimizer() {<a name="line.109"></a>
<FONT color="green">110</FONT>            setConvergenceChecker(new SimpleVectorialValueChecker());<a name="line.110"></a>
<FONT color="green">111</FONT>            setMaxIterations(DEFAULT_MAX_ITERATIONS);<a name="line.111"></a>
<FONT color="green">112</FONT>            setMaxEvaluations(Integer.MAX_VALUE);<a name="line.112"></a>
<FONT color="green">113</FONT>        }<a name="line.113"></a>
<FONT color="green">114</FONT>    <a name="line.114"></a>
<FONT color="green">115</FONT>        /** {@inheritDoc} */<a name="line.115"></a>
<FONT color="green">116</FONT>        public void setMaxIterations(int maxIterations) {<a name="line.116"></a>
<FONT color="green">117</FONT>            this.maxIterations = maxIterations;<a name="line.117"></a>
<FONT color="green">118</FONT>        }<a name="line.118"></a>
<FONT color="green">119</FONT>    <a name="line.119"></a>
<FONT color="green">120</FONT>        /** {@inheritDoc} */<a name="line.120"></a>
<FONT color="green">121</FONT>        public int getMaxIterations() {<a name="line.121"></a>
<FONT color="green">122</FONT>            return maxIterations;<a name="line.122"></a>
<FONT color="green">123</FONT>        }<a name="line.123"></a>
<FONT color="green">124</FONT>    <a name="line.124"></a>
<FONT color="green">125</FONT>        /** {@inheritDoc} */<a name="line.125"></a>
<FONT color="green">126</FONT>        public int getIterations() {<a name="line.126"></a>
<FONT color="green">127</FONT>            return iterations;<a name="line.127"></a>
<FONT color="green">128</FONT>        }<a name="line.128"></a>
<FONT color="green">129</FONT>    <a name="line.129"></a>
<FONT color="green">130</FONT>        /** {@inheritDoc} */<a name="line.130"></a>
<FONT color="green">131</FONT>        public void setMaxEvaluations(int maxEvaluations) {<a name="line.131"></a>
<FONT color="green">132</FONT>            this.maxEvaluations = maxEvaluations;<a name="line.132"></a>
<FONT color="green">133</FONT>        }<a name="line.133"></a>
<FONT color="green">134</FONT>    <a name="line.134"></a>
<FONT color="green">135</FONT>        /** {@inheritDoc} */<a name="line.135"></a>
<FONT color="green">136</FONT>        public int getMaxEvaluations() {<a name="line.136"></a>
<FONT color="green">137</FONT>            return maxEvaluations;<a name="line.137"></a>
<FONT color="green">138</FONT>        }<a name="line.138"></a>
<FONT color="green">139</FONT>    <a name="line.139"></a>
<FONT color="green">140</FONT>        /** {@inheritDoc} */<a name="line.140"></a>
<FONT color="green">141</FONT>        public int getEvaluations() {<a name="line.141"></a>
<FONT color="green">142</FONT>            return objectiveEvaluations;<a name="line.142"></a>
<FONT color="green">143</FONT>        }<a name="line.143"></a>
<FONT color="green">144</FONT>    <a name="line.144"></a>
<FONT color="green">145</FONT>        /** {@inheritDoc} */<a name="line.145"></a>
<FONT color="green">146</FONT>        public int getJacobianEvaluations() {<a name="line.146"></a>
<FONT color="green">147</FONT>            return jacobianEvaluations;<a name="line.147"></a>
<FONT color="green">148</FONT>        }<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>        /** {@inheritDoc} */<a name="line.150"></a>
<FONT color="green">151</FONT>        public void setConvergenceChecker(VectorialConvergenceChecker checker) {<a name="line.151"></a>
<FONT color="green">152</FONT>            this.checker = checker;<a name="line.152"></a>
<FONT color="green">153</FONT>        }<a name="line.153"></a>
<FONT color="green">154</FONT>    <a name="line.154"></a>
<FONT color="green">155</FONT>        /** {@inheritDoc} */<a name="line.155"></a>
<FONT color="green">156</FONT>        public VectorialConvergenceChecker getConvergenceChecker() {<a name="line.156"></a>
<FONT color="green">157</FONT>            return checker;<a name="line.157"></a>
<FONT color="green">158</FONT>        }<a name="line.158"></a>
<FONT color="green">159</FONT>    <a name="line.159"></a>
<FONT color="green">160</FONT>        /** Increment the iterations counter by 1.<a name="line.160"></a>
<FONT color="green">161</FONT>         * @exception OptimizationException if the maximal number<a name="line.161"></a>
<FONT color="green">162</FONT>         * of iterations is exceeded<a name="line.162"></a>
<FONT color="green">163</FONT>         */<a name="line.163"></a>
<FONT color="green">164</FONT>        protected void incrementIterationsCounter()<a name="line.164"></a>
<FONT color="green">165</FONT>            throws OptimizationException {<a name="line.165"></a>
<FONT color="green">166</FONT>            if (++iterations &gt; maxIterations) {<a name="line.166"></a>
<FONT color="green">167</FONT>                throw new OptimizationException(new MaxIterationsExceededException(maxIterations));<a name="line.167"></a>
<FONT color="green">168</FONT>            }<a name="line.168"></a>
<FONT color="green">169</FONT>        }<a name="line.169"></a>
<FONT color="green">170</FONT>    <a name="line.170"></a>
<FONT color="green">171</FONT>        /** <a name="line.171"></a>
<FONT color="green">172</FONT>         * Update the jacobian matrix.<a name="line.172"></a>
<FONT color="green">173</FONT>         * @exception FunctionEvaluationException if the function jacobian<a name="line.173"></a>
<FONT color="green">174</FONT>         * cannot be evaluated or its dimension doesn't match problem dimension<a name="line.174"></a>
<FONT color="green">175</FONT>         */<a name="line.175"></a>
<FONT color="green">176</FONT>        protected void updateJacobian() throws FunctionEvaluationException {<a name="line.176"></a>
<FONT color="green">177</FONT>            ++jacobianEvaluations;<a name="line.177"></a>
<FONT color="green">178</FONT>            jacobian = jF.value(point);<a name="line.178"></a>
<FONT color="green">179</FONT>            if (jacobian.length != rows) {<a name="line.179"></a>
<FONT color="green">180</FONT>                throw new FunctionEvaluationException(point, "dimension mismatch {0} != {1}",<a name="line.180"></a>
<FONT color="green">181</FONT>                                                      jacobian.length, rows);<a name="line.181"></a>
<FONT color="green">182</FONT>            }<a name="line.182"></a>
<FONT color="green">183</FONT>            for (int i = 0; i &lt; rows; i++) {<a name="line.183"></a>
<FONT color="green">184</FONT>                final double[] ji = jacobian[i];<a name="line.184"></a>
<FONT color="green">185</FONT>                final double factor = -Math.sqrt(weights[i]);<a name="line.185"></a>
<FONT color="green">186</FONT>                for (int j = 0; j &lt; cols; ++j) {<a name="line.186"></a>
<FONT color="green">187</FONT>                    ji[j] *= factor;<a name="line.187"></a>
<FONT color="green">188</FONT>                }<a name="line.188"></a>
<FONT color="green">189</FONT>            }<a name="line.189"></a>
<FONT color="green">190</FONT>        }<a name="line.190"></a>
<FONT color="green">191</FONT>    <a name="line.191"></a>
<FONT color="green">192</FONT>        /** <a name="line.192"></a>
<FONT color="green">193</FONT>         * Update the residuals array and cost function value.<a name="line.193"></a>
<FONT color="green">194</FONT>         * @exception FunctionEvaluationException if the function cannot be evaluated<a name="line.194"></a>
<FONT color="green">195</FONT>         * or its dimension doesn't match problem dimension or maximal number of<a name="line.195"></a>
<FONT color="green">196</FONT>         * of evaluations is exceeded<a name="line.196"></a>
<FONT color="green">197</FONT>         */<a name="line.197"></a>
<FONT color="green">198</FONT>        protected void updateResidualsAndCost()<a name="line.198"></a>
<FONT color="green">199</FONT>            throws FunctionEvaluationException {<a name="line.199"></a>
<FONT color="green">200</FONT>    <a name="line.200"></a>
<FONT color="green">201</FONT>            if (++objectiveEvaluations &gt; maxEvaluations) {<a name="line.201"></a>
<FONT color="green">202</FONT>                throw new FunctionEvaluationException(new MaxEvaluationsExceededException(maxEvaluations),<a name="line.202"></a>
<FONT color="green">203</FONT>                                                      point);<a name="line.203"></a>
<FONT color="green">204</FONT>            }<a name="line.204"></a>
<FONT color="green">205</FONT>            objective = f.value(point);<a name="line.205"></a>
<FONT color="green">206</FONT>            if (objective.length != rows) {<a name="line.206"></a>
<FONT color="green">207</FONT>                throw new FunctionEvaluationException(point, "dimension mismatch {0} != {1}",<a name="line.207"></a>
<FONT color="green">208</FONT>                                                      objective.length, rows);<a name="line.208"></a>
<FONT color="green">209</FONT>            }<a name="line.209"></a>
<FONT color="green">210</FONT>            cost = 0;<a name="line.210"></a>
<FONT color="green">211</FONT>            for (int i = 0, index = 0; i &lt; rows; i++, index += cols) {<a name="line.211"></a>
<FONT color="green">212</FONT>                final double residual = target[i] - objective[i];<a name="line.212"></a>
<FONT color="green">213</FONT>                residuals[i] = residual;<a name="line.213"></a>
<FONT color="green">214</FONT>                cost += weights[i] * residual * residual;<a name="line.214"></a>
<FONT color="green">215</FONT>            }<a name="line.215"></a>
<FONT color="green">216</FONT>            cost = Math.sqrt(cost);<a name="line.216"></a>
<FONT color="green">217</FONT>    <a name="line.217"></a>
<FONT color="green">218</FONT>        }<a name="line.218"></a>
<FONT color="green">219</FONT>    <a name="line.219"></a>
<FONT color="green">220</FONT>        /** <a name="line.220"></a>
<FONT color="green">221</FONT>         * Get the Root Mean Square value.<a name="line.221"></a>
<FONT color="green">222</FONT>         * Get the Root Mean Square value, i.e. the root of the arithmetic<a name="line.222"></a>
<FONT color="green">223</FONT>         * mean of the square of all weighted residuals. This is related to the<a name="line.223"></a>
<FONT color="green">224</FONT>         * criterion that is minimized by the optimizer as follows: if<a name="line.224"></a>
<FONT color="green">225</FONT>         * &lt;em&gt;c&lt;/em&gt; if the criterion, and &lt;em&gt;n&lt;/em&gt; is the number of<a name="line.225"></a>
<FONT color="green">226</FONT>         * measurements, then the RMS is &lt;em&gt;sqrt (c/n)&lt;/em&gt;.<a name="line.226"></a>
<FONT color="green">227</FONT>         * <a name="line.227"></a>
<FONT color="green">228</FONT>         * @return RMS value<a name="line.228"></a>
<FONT color="green">229</FONT>         */<a name="line.229"></a>
<FONT color="green">230</FONT>        public double getRMS() {<a name="line.230"></a>
<FONT color="green">231</FONT>            double criterion = 0;<a name="line.231"></a>
<FONT color="green">232</FONT>            for (int i = 0; i &lt; rows; ++i) {<a name="line.232"></a>
<FONT color="green">233</FONT>                final double residual = residuals[i];<a name="line.233"></a>
<FONT color="green">234</FONT>                criterion += weights[i] * residual * residual;<a name="line.234"></a>
<FONT color="green">235</FONT>            }<a name="line.235"></a>
<FONT color="green">236</FONT>            return Math.sqrt(criterion / rows);<a name="line.236"></a>
<FONT color="green">237</FONT>        }<a name="line.237"></a>
<FONT color="green">238</FONT>    <a name="line.238"></a>
<FONT color="green">239</FONT>        /**<a name="line.239"></a>
<FONT color="green">240</FONT>         * Get the Chi-Square value.<a name="line.240"></a>
<FONT color="green">241</FONT>         * @return chi-square value<a name="line.241"></a>
<FONT color="green">242</FONT>         */<a name="line.242"></a>
<FONT color="green">243</FONT>        public double getChiSquare() {<a name="line.243"></a>
<FONT color="green">244</FONT>            double chiSquare = 0;<a name="line.244"></a>
<FONT color="green">245</FONT>            for (int i = 0; i &lt; rows; ++i) {<a name="line.245"></a>
<FONT color="green">246</FONT>                final double residual = residuals[i];<a name="line.246"></a>
<FONT color="green">247</FONT>                chiSquare += residual * residual / weights[i];<a name="line.247"></a>
<FONT color="green">248</FONT>            }<a name="line.248"></a>
<FONT color="green">249</FONT>            return chiSquare;<a name="line.249"></a>
<FONT color="green">250</FONT>        }<a name="line.250"></a>
<FONT color="green">251</FONT>    <a name="line.251"></a>
<FONT color="green">252</FONT>        /**<a name="line.252"></a>
<FONT color="green">253</FONT>         * Get the covariance matrix of optimized parameters.<a name="line.253"></a>
<FONT color="green">254</FONT>         * @return covariance matrix<a name="line.254"></a>
<FONT color="green">255</FONT>         * @exception FunctionEvaluationException if the function jacobian cannot<a name="line.255"></a>
<FONT color="green">256</FONT>         * be evaluated<a name="line.256"></a>
<FONT color="green">257</FONT>         * @exception OptimizationException if the covariance matrix<a name="line.257"></a>
<FONT color="green">258</FONT>         * cannot be computed (singular problem)<a name="line.258"></a>
<FONT color="green">259</FONT>         */<a name="line.259"></a>
<FONT color="green">260</FONT>        public double[][] getCovariances()<a name="line.260"></a>
<FONT color="green">261</FONT>            throws FunctionEvaluationException, OptimizationException {<a name="line.261"></a>
<FONT color="green">262</FONT>    <a name="line.262"></a>
<FONT color="green">263</FONT>            // set up the jacobian<a name="line.263"></a>
<FONT color="green">264</FONT>            updateJacobian();<a name="line.264"></a>
<FONT color="green">265</FONT>    <a name="line.265"></a>
<FONT color="green">266</FONT>            // compute transpose(J).J, avoiding building big intermediate matrices<a name="line.266"></a>
<FONT color="green">267</FONT>            double[][] jTj = new double[cols][cols];<a name="line.267"></a>
<FONT color="green">268</FONT>            for (int i = 0; i &lt; cols; ++i) {<a name="line.268"></a>
<FONT color="green">269</FONT>                for (int j = i; j &lt; cols; ++j) {<a name="line.269"></a>
<FONT color="green">270</FONT>                    double sum = 0;<a name="line.270"></a>
<FONT color="green">271</FONT>                    for (int k = 0; k &lt; rows; ++k) {<a name="line.271"></a>
<FONT color="green">272</FONT>                        sum += jacobian[k][i] * jacobian[k][j];<a name="line.272"></a>
<FONT color="green">273</FONT>                    }<a name="line.273"></a>
<FONT color="green">274</FONT>                    jTj[i][j] = sum;<a name="line.274"></a>
<FONT color="green">275</FONT>                    jTj[j][i] = sum;<a name="line.275"></a>
<FONT color="green">276</FONT>                }<a name="line.276"></a>
<FONT color="green">277</FONT>            }<a name="line.277"></a>
<FONT color="green">278</FONT>    <a name="line.278"></a>
<FONT color="green">279</FONT>            try {<a name="line.279"></a>
<FONT color="green">280</FONT>                // compute the covariances matrix<a name="line.280"></a>
<FONT color="green">281</FONT>                RealMatrix inverse =<a name="line.281"></a>
<FONT color="green">282</FONT>                    new LUDecompositionImpl(MatrixUtils.createRealMatrix(jTj)).getSolver().getInverse();<a name="line.282"></a>
<FONT color="green">283</FONT>                return inverse.getData();<a name="line.283"></a>
<FONT color="green">284</FONT>            } catch (InvalidMatrixException ime) {<a name="line.284"></a>
<FONT color="green">285</FONT>                throw new OptimizationException("unable to compute covariances: singular problem");<a name="line.285"></a>
<FONT color="green">286</FONT>            }<a name="line.286"></a>
<FONT color="green">287</FONT>    <a name="line.287"></a>
<FONT color="green">288</FONT>        }<a name="line.288"></a>
<FONT color="green">289</FONT>    <a name="line.289"></a>
<FONT color="green">290</FONT>        /**<a name="line.290"></a>
<FONT color="green">291</FONT>         * Guess the errors in optimized parameters.<a name="line.291"></a>
<FONT color="green">292</FONT>         * &lt;p&gt;Guessing is covariance-based, it only gives rough order of magnitude.&lt;/p&gt;<a name="line.292"></a>
<FONT color="green">293</FONT>         * @return errors in optimized parameters<a name="line.293"></a>
<FONT color="green">294</FONT>         * @exception FunctionEvaluationException if the function jacobian cannot b evaluated<a name="line.294"></a>
<FONT color="green">295</FONT>         * @exception OptimizationException if the covariances matrix cannot be computed<a name="line.295"></a>
<FONT color="green">296</FONT>         * or the number of degrees of freedom is not positive (number of measurements<a name="line.296"></a>
<FONT color="green">297</FONT>         * lesser or equal to number of parameters)<a name="line.297"></a>
<FONT color="green">298</FONT>         */<a name="line.298"></a>
<FONT color="green">299</FONT>        public double[] guessParametersErrors()<a name="line.299"></a>
<FONT color="green">300</FONT>            throws FunctionEvaluationException, OptimizationException {<a name="line.300"></a>
<FONT color="green">301</FONT>            if (rows &lt;= cols) {<a name="line.301"></a>
<FONT color="green">302</FONT>                throw new OptimizationException(<a name="line.302"></a>
<FONT color="green">303</FONT>                        "no degrees of freedom ({0} measurements, {1} parameters)",<a name="line.303"></a>
<FONT color="green">304</FONT>                        rows, cols);<a name="line.304"></a>
<FONT color="green">305</FONT>            }<a name="line.305"></a>
<FONT color="green">306</FONT>            double[] errors = new double[cols];<a name="line.306"></a>
<FONT color="green">307</FONT>            final double c = Math.sqrt(getChiSquare() / (rows - cols));<a name="line.307"></a>
<FONT color="green">308</FONT>            double[][] covar = getCovariances();<a name="line.308"></a>
<FONT color="green">309</FONT>            for (int i = 0; i &lt; errors.length; ++i) {<a name="line.309"></a>
<FONT color="green">310</FONT>                errors[i] = Math.sqrt(covar[i][i]) * c;<a name="line.310"></a>
<FONT color="green">311</FONT>            }<a name="line.311"></a>
<FONT color="green">312</FONT>            return errors;<a name="line.312"></a>
<FONT color="green">313</FONT>        }<a name="line.313"></a>
<FONT color="green">314</FONT>    <a name="line.314"></a>
<FONT color="green">315</FONT>        /** {@inheritDoc} */<a name="line.315"></a>
<FONT color="green">316</FONT>        public VectorialPointValuePair optimize(final DifferentiableMultivariateVectorialFunction f,<a name="line.316"></a>
<FONT color="green">317</FONT>                                                final double[] target, final double[] weights,<a name="line.317"></a>
<FONT color="green">318</FONT>                                                final double[] startPoint)<a name="line.318"></a>
<FONT color="green">319</FONT>            throws FunctionEvaluationException, OptimizationException, IllegalArgumentException {<a name="line.319"></a>
<FONT color="green">320</FONT>    <a name="line.320"></a>
<FONT color="green">321</FONT>            if (target.length != weights.length) {<a name="line.321"></a>
<FONT color="green">322</FONT>                throw new OptimizationException("dimension mismatch {0} != {1}",<a name="line.322"></a>
<FONT color="green">323</FONT>                                                target.length, weights.length);<a name="line.323"></a>
<FONT color="green">324</FONT>            }<a name="line.324"></a>
<FONT color="green">325</FONT>    <a name="line.325"></a>
<FONT color="green">326</FONT>            // reset counters<a name="line.326"></a>
<FONT color="green">327</FONT>            iterations           = 0;<a name="line.327"></a>
<FONT color="green">328</FONT>            objectiveEvaluations = 0;<a name="line.328"></a>
<FONT color="green">329</FONT>            jacobianEvaluations  = 0;<a name="line.329"></a>
<FONT color="green">330</FONT>    <a name="line.330"></a>
<FONT color="green">331</FONT>            // store least squares problem characteristics<a name="line.331"></a>
<FONT color="green">332</FONT>            this.f         = f;<a name="line.332"></a>
<FONT color="green">333</FONT>            jF             = f.jacobian();<a name="line.333"></a>
<FONT color="green">334</FONT>            this.target    = target.clone();<a name="line.334"></a>
<FONT color="green">335</FONT>            this.weights   = weights.clone();<a name="line.335"></a>
<FONT color="green">336</FONT>            this.point     = startPoint.clone();<a name="line.336"></a>
<FONT color="green">337</FONT>            this.residuals = new double[target.length];<a name="line.337"></a>
<FONT color="green">338</FONT>    <a name="line.338"></a>
<FONT color="green">339</FONT>            // arrays shared with the other private methods<a name="line.339"></a>
<FONT color="green">340</FONT>            rows      = target.length;<a name="line.340"></a>
<FONT color="green">341</FONT>            cols      = point.length;<a name="line.341"></a>
<FONT color="green">342</FONT>            jacobian  = new double[rows][cols];<a name="line.342"></a>
<FONT color="green">343</FONT>    <a name="line.343"></a>
<FONT color="green">344</FONT>            cost = Double.POSITIVE_INFINITY;<a name="line.344"></a>
<FONT color="green">345</FONT>    <a name="line.345"></a>
<FONT color="green">346</FONT>            return doOptimize();<a name="line.346"></a>
<FONT color="green">347</FONT>    <a name="line.347"></a>
<FONT color="green">348</FONT>        }<a name="line.348"></a>
<FONT color="green">349</FONT>    <a name="line.349"></a>
<FONT color="green">350</FONT>        /** Perform the bulk of optimization algorithm.<a name="line.350"></a>
<FONT color="green">351</FONT>         * @return the point/value pair giving the optimal value for objective function<a name="line.351"></a>
<FONT color="green">352</FONT>         * @exception FunctionEvaluationException if the objective function throws one during<a name="line.352"></a>
<FONT color="green">353</FONT>         * the search<a name="line.353"></a>
<FONT color="green">354</FONT>         * @exception OptimizationException if the algorithm failed to converge<a name="line.354"></a>
<FONT color="green">355</FONT>         * @exception IllegalArgumentException if the start point dimension is wrong<a name="line.355"></a>
<FONT color="green">356</FONT>         */<a name="line.356"></a>
<FONT color="green">357</FONT>        abstract protected VectorialPointValuePair doOptimize()<a name="line.357"></a>
<FONT color="green">358</FONT>            throws FunctionEvaluationException, OptimizationException, IllegalArgumentException;<a name="line.358"></a>
<FONT color="green">359</FONT>    <a name="line.359"></a>
<FONT color="green">360</FONT>    }<a name="line.360"></a>




























































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